Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



A simple proof for the existence of Zariski decompositions on surfaces

Author: Thomas Bauer
Journal: J. Algebraic Geom. 18 (2009), 789-793
Published electronically: March 4, 2008
MathSciNet review: 2524598
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Abstract: In this note we give a quick and simple proof of the existence (and uniqueness) of Zariski decompositions on surfaces. While Zariski's original proof employs a rather sophisticated procedure to construct the negative part of the decomposition, the present approach is based on the idea that the positive part can be constructed from a maximality condition. It may also be useful that this approach yields a practical algorithm for the computation of the positive part.

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Thomas Bauer
Affiliation: Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Straße, D-35032 Marburg, Germany

Received by editor(s): August 9, 2007
Received by editor(s) in revised form: November 7, 2007
Published electronically: March 4, 2008
Additional Notes: The author was partially supported by DFG grant BA1559/4-3

American Mathematical Society